Deep Learning and genetic algorithms for cosmological Bayesian inference speed-up

TL;DR

This paper presents a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process.

Abstract

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a robust framework for extracting theoretical insights from observational data. However, its computational demands can be substantial, primarily due to the need for numerous likelihood function evaluations. Our proposed method utilizes the power of deep learning, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process. Unlike traditional approaches, our method trains neural networks on-the-fly using the current set of live points as training data, without the need for pre-training. This flexibility enables adaptation to various theoretical models and datasets. We perform simple hyperparameter optimization using genetic algorithms to suggest initial neural network architectures for learning each likelihood function. Once sufficient accuracy is achieved, the neural network replaces the original likelihood function. The implementation integrates with nested sampling algorithms and has been thoroughly evaluated using both simple cosmological dark energy models and diverse observational datasets. Additionally, we explore the potential of genetic algorithms for generating initial live points within nested sampling inference, opening up new avenues for enhancing the efficiency and effectiveness of Bayesian inference methods.

Figures (4)

• Figure 1: Comparison of neural likelihoods versus original likelihoods using toy models. Using 1000 live points.
• Figure 2: Case 1. Posterior plots for CPL Pantheon+HD+BAO with the proposed methods in this work.
• Figure 3: Case 2. Posterior plots for CPL using Pantheon+HD+BAO with the proposed methods in this work. We use 4000 live points.
• Figure 4: Case 3. 2D posterior plots for CPL with curvature using Pantheon+HD+BAO+f$\sigma_8$+Planck with the proposed methods in this work. Using 4000 points and considering 8 free parameters. In this case, because of the complexity, there were three neural networks trained before to substitute the likelihood function, however, the Bayesian inference process using our method was 19.6% faster.